Model-based diagnostics post-processing for fast automated model building; show-cased with residual error models and CWRES.
Moustafa M.A. Ibrahim (1), Rikard Nordgren (1), Maria C. Kjellsson (1), Mats O. Karlsson (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Sweden
Background and Objectives: Graphical diagnostics often provide useful indication of model misspecification. Here we investigate if model-based post-processing of common diagnostics, can provide additional advantages. We have selected to show-case this principle with CWRES [1], and residual error (RUV) models, where the new diagnostic tool is used to scan seven extended RUV models [2-4]: between-variable-(L2)-correlation, interindividual variability (IIV) on RUV, power model, time varying error magnitude, autocorrelated errors, t-distributed errors, and dynamic transform both sides (dTBS).
Methods: CWRES outputted from the original model, expected to be distributed N(0,1) for a correct model, were treated as dependent variable DV and modelled by a base model: y=Θ+?+?. The base model was then extended with the different RUV models, and used to model CWRES, e.g. IIV on RUV: y= Θ+?1+?*exp (?2). ΔOFV was calculated for each extended RUV model as the difference between base model objective function value OFV and extended RUV model OFV. The agreement, in ΔOFV between implementing these extended RUV models on the original model (conventional analysis) and just doing it on the CWRES, was evaluated in both real (n=15) and simulated (n=7) data examples.
Results: The agreement in improvement in fit (dOFV) between the original and CWRES models was high for all 7 RUV extensions (r across all models = 0.88 with an average ratio of ΔOFVs of 0.92) and the typical improvement was substantial (average (median) dOFV across all models = -220 (-70)). Also the parameters governing the extended RUV showed good concordance between the estimates obtained in the CWRES and original models. The simulated examples further supported a good agreement between the true misspecification in error model and what was identified by modelling of CWRES.
Conclusions: CWRES modelling is a promising, fast and easily automated diagnostic tool for model development process. It provides guidance for the nature and magnitude of potential model misspecification/improvements. It can be easily implemented in analysis software and is already implemented as resmod tool in PsN.
References:
[1] Hooker, A. C., Staatz, C. E., & Karlsson, M. O. (2007). Conditional Weighted Residuals (CWRES): A Model Diagnostic for the FOCE Method. Pharmaceutical Research, 24(12), 2187-2197
[2] Karlsson, M. O., Beal, S. L., & Sheiner, L. B. (1995). Three new residual error models for population PK/PD analyses. Journal of Pharmacokinetics and Biopharmaceutics, 23(6), 651-672.
[3] Karlsson, M.O., Jonsson, E. N., Wiltse, C.G & Wade, J.R. (1998). Assumption Testing in Population Pharmacokinetic Models: Illustrated with an Analysis of Moxonidine Data from Congestive Heart Failure Patients. Journal of Pharmacokinetics and Biopharmaceutics, 26(2),207-246.
[4] Dosne, A., Bergstrand, M., & Karlsson, M. O. (2015). A strategy for residual error modeling incorporating scedasticity of variance and distribution shape. Journal of Pharmacokinetics and Pharmacodynamics, 43(2), 137-151.
